In a TEM an object, also referred to as a sample, is irradiated with a beam of electrons, the electrons having an energy of e.g. between 50 keV and 400 keV. Some of the electrons are transmitted through the sample, and these electrons are focused on the image plane to form an enlarged image of the sample. The imaging of the sample on the image plane is realized with a projection system, that can be set to a configurable magnification of e.g. between 103 and 106 times. Typically a detector, such as a CCD camera or CMOS camera, is placed in the image plane, whereby the image is detected. Such detector may e.g. have a semiconductor sensor having 4 k×4 k pixels arranged in a two-dimensional array. With such detector, the electrons impinge on the semiconductor chip of the CCD or CMOS sensor and generate electron hole pairs, thereby forming the charge to be detected by the CCD or CMOS chip.
For some applications, a very low dose of electrons is required. For example, biological materials may already degrade at doses of 10-30 electrons per 0.1 nm×0.1 nm within a frame time of 8-10 seconds. This may result in an average dose of 0.001-0.1 electrons per pixel or even less at the detector. Although CCD and CMOS cameras are constantly improving, Signal to Noise Ratio (SNR) and Modulation Transfer Function (MTF) may still be limiting the performance of the detector. For an exemplary direct electron detection CMOS camera in a TEM, one incident electron may generate thousands of electron hole pairs which diffuse over an area of e.g. 5×5 pixels and finally generate about a total of 240 output signal counts in the 5×5 pixels. As a result, the Point Spread Function (PSF) may be significant larger than the spatial sampling dimensions (one pixel). In the following, any reference to the length of the PSF may refer to the width of the PSF in terms of number of pixels: the length is five when the electron hole pairs diffuse over an area of 5×5 pixels. At halve-Nyquist frequency of the sensor, an MTF less than 0.5 is achieved. The MTF at Nyquist is approaching to zero. This results in a loss of MTF and thus resolution. Secondly, the peak count at the center pixel may be roughly 30 counts, while the dark current noise of the semiconductor sensor may typically vary between 0 and 30 counts. This results in an SNR around 1. At these low doses, both SNR and MTF determine the image quality. Due to the relatively high noise level, known image improvement technologies like image deconvolution are not very successful to recover from this noise and point spread function. Besides the dark current noise, also the number of electron hole pairs that are being generated in the semiconductor sensor for a single incident electron, and thus of the deposited energy per electron, may vary wildly and affect the SNR. One incident electron of 300 keV may e.g. result in any number of electron hole pairs between 0 and 80.000 and a corresponding spread in detected charge. In the following, the charge detected by a pixel of the semiconductor chip will be represented by a corresponding pixel signal with a signal strength representing a certain number of signal counts.
It is known to determine whether an electron is present on a pixel by comparing the pixel signal to a predetermined reference level in so-called threshold detection. However, such threshold detection may result in many misdetections when the dose is low and when the SNR around 1.
To overcome the effects of the Point Spread Function, it has been proposed to use Partial Response (PR) detection, using a Partial Response function resembling the Point Spread Function. For binary images, a Partial Response Maximum Likelihood (PRML) detection and Viterbi Detection have been proposed with success. However, the inventor has found that such known methods do not give a satisfactory results when applied to an image obtained in a TEM, especially not in the presence of SNR is around 1 and/or when the spread in signal counts for a single incident electron is large.
A disadvantage of the aforementioned methods is that the achievable resolution may be compromised. Especially when the dose is low, it may not be possible to determine the number of incident electrons on each pixel with a sufficient reliability.
Accordingly, there is a need to provide a method wherein the quality of an image acquired by a detector in a particle-optical apparatus, such as a TEM, is improved, especially at low dose and where the signal of a single incident particle, such as an electron, is spread over a plurality of pixels, e.g. due to diffusion in the semiconductor sensor.